Chapter 22: Ratio, Proportion and Proof

Ratios are used to compare quantities

You can find equivalent ratios by multiplying or dividing by the same number

To write a ratio in its simplest form, find an equivalent ratio with the smallest possible whole number values

If you use x to represent one part of the ratio, then you can write the length of the x as x

Then form an equation and solve it to find x

If the ratio contains decimals or fractions-multiply

If the ratio has mixed units-convert to the smaller unit

Two quantities are in direct proportion when both quantities increase at the same rate

Two quantities are in inverse proportion when one quantity increases at the same rate as the other quantity decreases

You can use common sense to work out whether to divide or multiply in proportion questions

6 people build a wall in 4 days

6x4=24 so 1 person could build the wall in 24 days

24/8=3 so 8 people could build the wall in 3 days

Show your method by writing down what you are working out at each stage of your working

Read the question carefully-you have to write down the option which offers better value

You won’t get the final mark if you just circle or underline your choice

You can use algebra to prove facts about numbers

Using algebra helps you to probe that something is true for every number

In a proof question the working is the answer

If the question say ‘show that’ or ‘prove that’ you need to write down every stage of your working

If you don’t you won’t get all the marks

If you need to prove something about numbers then you always use algebra

Even number = 2n

Odd number = 2n+1 or 2n-1

Multiple of 3 = 3n

Consecutive numbers = n,n+1.n+2…

Consecutive even numbers = 2n,2n+2,2n+4…

Consecutive odd numbers = 2n+1,2n+3,2n+5…

Ratios are used to compare quantities

You can find equivalent ratios by multiplying or dividing by the same number

To write a ratio in its simplest form, find an equivalent ratio with the smallest possible whole number values

If you use x to represent one part of the ratio, then you can write the length of the x as x

Then form an equation and solve it to find x

If the ratio contains decimals or fractions-multiply

If the ratio has mixed units-convert to the smaller unit

Two quantities are in direct proportion when both quantities increase at the same rate

Two quantities are in inverse proportion when one quantity increases at the same rate as the other quantity decreases

You can use common sense to work out whether to divide or multiply in proportion questions

6 people build a wall in 4 days

6x4=24 so 1 person could build the wall in 24 days

24/8=3 so 8 people could build the wall in 3 days

Show your method by writing down what you are working out at each stage of your working

Read the question carefully-you have to write down the option which offers better value

You won’t get the final mark if you just circle or underline your choice

You can use algebra to prove facts about numbers

Using algebra helps you to probe that something is true for every number

In a proof question the working is the answer

If the question say ‘show that’ or ‘prove that’ you need to write down every stage of your working

If you don’t you won’t get all the marks

If you need to prove something about numbers then you always use algebra

Even number = 2n

Odd number = 2n+1 or 2n-1

Multiple of 3 = 3n

Consecutive numbers = n,n+1.n+2…

Consecutive even numbers = 2n,2n+2,2n+4…

Consecutive odd numbers = 2n+1,2n+3,2n+5…